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1 This question concerns the solution of the equation e" = 2x. (a) By sketching a suitable graph, show that this equation has a solution somewhere between x = 0 and x = 1.

1 This question concerns the solution of the equation e" = 2x. (a) By sketching a suitable graph, show that this equation has a solution somewhere between x = 0 and x = 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(b) The first three non-zero terms of the power series expansion of e* are 1-x+x²/2. (i) (ii) Page 3 of 22 By using the first two terms only, show that an approximation of the solution is x= 1/3. If the third term of the power series is included, show that the solution is approximately x≈3-√7. Turn the page over
Transcribed Image Text:(b) The first three non-zero terms of the power series expansion of e* are 1-x+x²/2. (i) (ii) Page 3 of 22 By using the first two terms only, show that an approximation of the solution is x= 1/3. If the third term of the power series is included, show that the solution is approximately x≈3-√7. Turn the page over
1 This question concerns the solution of the equation e = 2x. (a) By sketching a suitable graph, show that this equation has a solution somewhere between x = 0 and x = 1.
Transcribed Image Text:1 This question concerns the solution of the equation e = 2x. (a) By sketching a suitable graph, show that this equation has a solution somewhere between x = 0 and x = 1.
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